First slide

Rectilinear Motion

Question

A helicopter is ascending vertically with a speed of 8m/s. At a height of 120m above the earth, a stone is dropped from a window. How much time does it take for the stone to reach the ground.

Moderate

Solution

Initial speed $u = 8 m / s$
Height $h = 120 m$
From equation of height of tower
$\begin{array}{l} h = \frac{1}{2} g t^{2} - u t \\ \Rightarrow 120 = \frac{1}{2} \times 9.8 \times t^{2} - 8 t \\ \Rightarrow 4.9 t^{2} - 8 t - 120 = 0 \\ t = \frac{8 \pm \sqrt{64 + 4 \times 4.9 \times 120}}{2 \times 4.9} \\ t = \frac{8 \pm 49.15}{9.8} \\ t = 5.83 s (only positive value) \end{array}$

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